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On Duality and the Bi-Conjugate Gradient Algorithm

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Harnett, Kristin E. (2008) On Duality and the Bi-Conjugate Gradient Algorithm. Master's Thesis, University of Pittsburgh. (Unpublished)

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Abstract

It is not uncommon to encounter problems that lead to large, sparse linear systems with coefficient matrices that are invertible and sparse, but have little other structure. In such problems the solution u=A¹ƒ is typically calculated only to acurately compute functionals of the solution, L(u). This paper determines a method that converges rapidly to the functional's value. Specifially, a modified bi-conjugate gradient algorithm is found to generate convergence to the solution of linear functionals, L(u), much more rapidly than convergence to the linear system solution u.


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Details

Item Type: University of Pittsburgh ETD
Status: Unpublished
Creators/Authors:
CreatorsEmailPitt UsernameORCID
Harnett, Kristin E.kehst42@pitt.eduKEHST42
ETD Committee:
TitleMemberEmail AddressPitt UsernameORCID
Committee ChairLayton, Williamwjl@pitt.eduWJL
Committee MemberRebholz, Leo
Committee MemberSussman, Mike
Date: 28 September 2008
Date Type: Completion
Defense Date: 24 April 2008
Approval Date: 28 September 2008
Submission Date: 27 July 2008
Access Restriction: No restriction; Release the ETD for access worldwide immediately.
Institution: University of Pittsburgh
Schools and Programs: Dietrich School of Arts and Sciences > Mathematics
Degree: MS - Master of Science
Thesis Type: Master's Thesis
Refereed: Yes
Uncontrolled Keywords: bi-conjugate gradient; biconjugate gradient; duality; functionals; iterative methods; sparse systems
Other ID: http://etd.library.pitt.edu/ETD/available/etd-07272008-001302/, etd-07272008-001302
Date Deposited: 10 Nov 2011 19:54
Last Modified: 15 Nov 2016 13:47
URI: http://d-scholarship.pitt.edu/id/eprint/8654

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